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In this triangular prism, we are asked to identify which lines are parallel.

### Understanding the Geometry of a Triangular Prism:
- A triangular prism consists of two triangular faces and three rectangular faces.
- Parallel lines in a prism generally run along the same direction on opposite sides of the prism.

Looking at the diagram:

1. **DE and BA**: These lines are on different planes. Line \( DE \) lies on the bottom triangle, while line \( BA \) is part of the top triangle. Hence, they are **not parallel**.
   
2. **CD and BA**: Similar to the previous case, \( CD \) is part of the bottom triangle, and \( BA \) is part of the top triangle. These are also on different planes and hence **not parallel**.

3. **AD and BC**: These two lines are part of the same rectangular face and run in the same direction. Therefore, they **are parallel**.

4. **AD and AE**: These lines are connected by the common vertex \( A \) and form an angle, so they cannot be parallel. They are **not parallel**.

### Correct Answer:
The correct pair of parallel lines is **AD and BC**.

Would you like a deeper explanation of any part of this? Here are 5 related questions to explore:

1. What are the properties of parallel lines in three-dimensional geometry?
2. How can we determine parallelism in complex polyhedra?
3. What distinguishes a triangular prism from other prisms geometrically?
4. Can two lines in different planes ever be parallel?
5. How does the direction of lines help in identifying parallelism?

**Tip:** When determining parallelism in a 3D shape, check if the lines lie on the same plane or in parallel planes and run in the same direction!

Which lines are parallel in the triangular prism? Select each correct answer.

Learn how to determine which lines are parallel in a triangular prism using 3D geometry principles. This problem focuses on understanding geometric properties of prisms and identifying parallel lines. Suitable for students in Grades 7-9.

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